Drive feedthrough nulling system

ABSTRACT

The present invention relates to a system for nulling drive feedthrough error in a sensor having first and second drive electrodes which impart vibratory motion to first and second proof masses in response to first and second opposite phase drive signals, and having first and second capacitances defined between the drive electrodes and their associated proof masses. A mismatch between the first and the second capacitance is measured. Drive feedthrough caused by the measured capacitance mismatch is nulled by adjusting the relative amplitudes of the first and second opposite phase drive signals, whereby the ratio of the amplitudes is proportional to the ratio of the first and second capacitances. A servo loop may adaptively effect the ratio of amplitudes.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] Not Applicable

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] Not Applicable

REFERENCE TO MICROFICHE APPENDIX

[0003] Not Applicable

FIELD OF THE INVENTION

[0004] This invention relates generally to feedthrough nulling systems,and more particularly to systems for nulling drive signal feedthrough insensors.

BACKGROUND OF THE INVENTION

[0005] Coriolis force sensors such as tuning-fork gyroscopes are knownin the art. These sensors can be fabricated using MEMS(microelectromechanical systems) techniques, by way of example.Micromachined Coriolis force sensors generally include a pair of proofmasses which are positioned on opposite sides of an input axis, andwhich are connected to a substrate by support flexures. The flexuressupport the proof masses so as to allow the proof masses to vibrate in anominal plane that includes the input axis. Time varying drive signalsare provided by way of drive electrodes to impart an in-plane,anti-parallel vibratory motion to the proof masses. Typically, thefrequency of the drive signals is set at or near the mechanical resonantfrequency of the sensor assembly.

[0006] Position sensitive in-plane pick-off electrodes are usuallyprovided for sensing in-plane displacements of the proof masses causedby the vibratory motion. The pick-off electrodes are coupled to afeedback gain control circuit, which controls the amplitude of the drivesignals, and thus the amplitude of vibration of the proof masses. Forstable and predictable gyroscope performance, the amplitude of vibrationof the proof masses is preferably maintained at a predetermined,constant level.

[0007] Upon rotation of the sensor assembly about the input axis, thevibrating proof masses produce anti-parallel, out-of-plane deflections,caused by Coriolis forces which arise in response to the rotation.Out-of-plane sensing electrodes are provided in order to detect theout-of-plane deflections. Due to the nature of the Coriolis force, whosemagnitude depends on the rotational rate of the sensor assembly, theamplitudes of the Coriolis deflections are proportional to therotational rate of the sensor about the input axis. The sensingelectrodes thus generate a signal indicative of the rotational rate ofthe gyroscope.

[0008] The performance of sensors such as the tuning fork gyroscopediscussed above is adversely affected by a feedthrough of the drivesignals into the sensor output, resulting from a coupling of signalsfrom the drive electrodes into the out-of-plane sensing electrodes.Drive feedthrough affects measurements by both the out-of-plane sensingelectrodes and the in-plane pick-off electrodes, thus limiting gyroscopeperformance.

[0009] It is an object of this invention to provide a system forsignificantly reducing drive feedthrough, thereby improving sensorperformance.

SUMMARY OF THE INVENTION

[0010] The present invention relates to a system for nulling drivefeedthrough error in sensors such as tuning fork gyroscopes. By reducingthe undesirable effects of drive feedthrough, the present inventionreduces one of the largest electronic sources of error in tuning forkgyroscopes. Further, the technique of the present invention has generalapplicability, and can be used to null other forms of drive feedthrough.

[0011] In one embodiment, the present invention relates to a system fornulling feedthrough error in a sensor having first and second driveelectrodes which impart vibratory motion to first and second proofmasses in response to first and second opposite phase drive signals, andhaving capacitances defined between the drive electrodes and theirassociated proof masses. The present invention is predicated in part onthe recognition that capacitance mismatch between the drive electrodesand the associated proof masses is a dominant cause of drive feedthroughin Coriolis force sensors.

[0012] In accordance with the present invention, a differential driveamplitude is adjusted in order to compensate for drive capacitancemismatch. Compensation is accomplished by measuring the capacitancemismatch between the first and second drive electrodes and theirassociated proof masses, and nulling the measured capacitance mismatchby adjusting the drive signals. The capacitance mismatch can be measuredby detecting signals that are proportional to the capacitance mismatch.In one embodiment, an off-frequency artifact is detected in order toobtain a measure of the drive capacitance mismatch.

[0013] In accordance with the present invention, a sensor for detectinga rotational rate about an input axis includes a substrate, and firstand second proof masses positioned on opposite sides of an input axis.The proof masses are flexurally coupled to the substrate so as to permitan in-plane vibratory motion of the masses in a nominal plane includingthe input axis, and an out-of-plane vibratory motion in a directionperpendicular to the nominal plane. Each proof mass includes aelectronically conductive region.

[0014] A driver includes first and second drive electrodes opposite theelectrically conductive regions of the first and second proof masses.First and second capacitances are defined between the first driveelectrode and the first proof mass, and between the second driveelectrode and the second proof mass, respectively. The first and seconddrive electrodes are adapted to receive first and second a.c. oppositephase electrical drive signals for electrostatically driving the firstand second proof masses to effect the anti-parallel vibration in thenominal plane. The frequency of the drive signals is preferably set tobe substantially equal to a fundamental frequency corresponding to amechanical resonant frequency of the sensor.

[0015] First and second sensing electrodes are provided for detectingthe out of plane vibratory motion perpendicular to the nominal plane,arising from the Coriolis force that acts upon the proof masses when thesensor assembly rotates about the input axis. Each sensing electrode isfixedly positioned with respect to the substrate, and is disposedopposite the conductive region on a respective one of the first andsecond proof masses. The sensor is preferably micromachined, i.e. theproof masses, the drive electrodes, and the sensing electrodes are madefrom an etched silicon structure.

[0016] A circuit generates an output signal corresponding to theseparation between the sensing electrodes and the conductive regions ofthe proof masses opposite. The output signal is representative of therotational rate of the sensor about the input axis. Means are providedfor adjusting the relative amplitudes of the first and second a.c. drivesignals, whereby the ratio of the amplitudes is proportional to theratio of the first and second capacitances. The adjustment of relativeamplitudes of the drive signals substantially nulls drive feedthrough inthe output signal caused by a mismatch in the first and secondcapacitances. In particular, when the drive signals have oppositepolarities, and have a magnitude ratio equal to the reciprocal of theratio of the corresponding capacitances, drive feedthrough from drivecapacitance mismatch is substantially nulled.

[0017] The circuit may include first and second circuits. The firstcircuit is operative to provide an indicative signal proportional to acapacitance mismatch between the first and second capacitances. Thesecond circuit is operative to measure the capacitance mismatch usingthe indicative signal, and to compensate for the measured capacitancemismatch by adjusting the first and second drive signals so as tosubstantially null drive feedthrough.

[0018] The first circuit may include a sense preamplifier connected tothe proof masses. The output from the sense preamplifier contains asignal that is indicative of the mismatch between the first and secondcapacitances. The indicative signal can be demodulated in the secondcircuit to obtain a measure of the drive capacitance mismatch. Theindicative signal may be a separate tracer signal that has been added tothe drive signals. Alternatively, the indicative signal may be aninherent off-frequency component of the drive signal, in which thesensor resonant frequency and its harmonics have been suppressed.

[0019] The second circuit may include an adjustment device responsive toa controller for effecting the ratio of amplitudes, and a servo loop foradaptively effecting the ratio of amplitudes. In one embodiment, theadjustment device includes first and second variable gain amplifiers(VGAs) interposed between the servo loop and the first and second driveelectrodes. The VGAs are operative to adjust the differential amplitudeof the drive signals in response to the controller.

[0020] The second circuit may include means for demodulating theindicative signal from the first circuit so as to obtain a DC signalproportional to the capacitance mismatch. In one embodiment, the meansfor demodulating the indicative signal may include a multiplier, a lowpass filter for removing modulation components from the indicativesignal, and a controller. The demodulated signal may be passed throughthe controller to provide a control signal. The control signal may besplit into first and second control signals of opposite phase, whichcontrol the first and second VGAs, respectively.

[0021] The present invention also relates to a method for nulling drivefeedthrough in a sensor having first and second drive electrodes whichimpart vibratory motion to first and second members in response to firstand second drive signals, and having first and second capacitancesdefined between the first and second drive electrodes and theirassociated proof masses. A mismatch between the first capacitance andthe second capacitance is measured. Drive feedthrough caused by themismatch is nulled by compensating for the measured capacitancemismatch. The relative amplitudes of the first and second drive signalsis adjusted in order to compensate for the measured capacitancemismatch.

BRIEF DESCRIPTION OF THE DRAWING

[0022] Other features and advantages of the present invention will beapparent from the following detailed description of the drawing inwhich:

[0023]FIG. 1 is a perspective view of a prior art Coriolis sensor.

[0024] FIGS. 2(a) and 2(b) illustrate a drive coupling model for thesensor of FIG. 1.

[0025]FIG. 3 is a diagram of an automatic drive feedthrough nullingsystem, in accordance with the present invention, for the sensor of FIG.1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0026]FIG. 1 illustrates a prior art sensor 10, such as amicromechanical tuning-fork gyroscope, for detecting a rotational rateabout an input axis 11 of the sensor 10. The sensor 10 includes asubstrate 32, and first 20 and second 22 proof masses positioned onopposite sides of the input axis 11. The proof masses 20 and 22 areflexurally coupled to the substrate 32 by means of support flexures 30.In one embodiment, the proof masses 20 and 22 are suspended by theflexures 30 above the substrate 32, so as to permit vibratory motion ofthe proof masses in-plane in a nominal plane including the input axis,as well as out-of-plane in a direction perpendicular to the nominalplane. The nominal plane may be parallel to the surface of the substrate32. Each proof mass includes an electrically conductive region, shown as21 a and 21 b, respectively.

[0027] The prior art sensor 10 includes a driver having first 14 andsecond 16 drive electrodes disposed opposite the electrically conductiveregions 21 a, 21 b of the first 20 and second 22 proof masses. Thesensor 10 also includes first 24 and second 26 out-of-plane sensingelectrodes, and an in-plane position-sensitive pickoff electrode 28. Inone embodiment, the in-plane pickoff electrode 28 is also suspendedabove the substrate 32 by the flexures 30, while the out-of-planesensing electrodes 24 and 26 are disposed on the substrate 32.

[0028] In one embodiment, each proof mass has comb electrodes 18extending laterally therefrom and toward an adjacent one of the driveelectrodes. The drive electrodes 14, 16 have complementary combelectrodes 18 extending toward, and interleaved with, the combelectrodes 18 of the adjacent one of the proof masses 20 and 22. Thedrive electrodes 14 and 16 are electrostatically coupled to the proofmasses 20 and 22, respectively, by the sets of interleaved combelectrodes 18. First and second capacitances C₁ and C₂ are thus definedbetween the first 14 and second 16 drive electrodes, and the first 20and second 22 proof masses, respectively.

[0029] The first and second drive electrodes 14 and 16 are adapted toreceive first and second a.c. opposite phase electrical drive signalswhich induce electrostatic forces between the sets of interleaved combelectrodes 18 between electrode 14 and proof mass 20 on the one hand andelectrode 16 and proof mass 22 on the other. The drive signals typicallyare square waves. The drive electrodes convert the drive signal into anelectrostatic Coulomb force signal proportional to the square of thedrive signal, thereby electrostatically driving the proof masses toimpart in-plane vibration to the proof masses in the nominal plane (inthe directions shown by arrows 15).

[0030] In response to a rotation of the sensor 10 about the input axis11, the proof masses deflect out of the plane of vibration. Suchout-of-plane deflections of the proof masses 20, 22 occur because of theCoriolis forces that arise from the rotation around the input axis andact on the moving proof masses. The Coriolis force is given by:

{right arrow over (F)}=−2m{right arrow over (Ω)}×{right arrow over(V)}  Eq. 1

[0031] where

[0032] m=mass of the proof mass,

[0033] {right arrow over (Ω)}=angular velocity of the proof mass aboutthe input axis,

[0034] {right arrow over (V)}=velocity of in-plane vibration of theproof mass, and

[0035] x denotes the vector cross-product.

[0036] Since the in-plane vibrations occur at a drive frequency, fromEq. 1 it follows that the out-of-plane deflections of the proof massesalso occur at the drive frequency. The drive frequency is typically setto be substantially equal to the mechanical resonant frequency of thesensor, generally referred to as the fundamental frequency.

[0037] In order to maintain stable gyroscope performance, the vibratoryamplitudes of the proof masses 20, 22 should be kept relativelyconstant. This is accomplished by monitoring the in-plane proof massdeflection with the position sensitive pick-off electrode 28. Thepick-off electrode 28 produces an output signal which is indicative ofthe amplitude of the in-plane motion of the proof masses. The outputsignal from the pick-off electrode 28 is fed to a feedback gain controlloop to control the amplitudes of the drive signals, and thus theamplitudes of the vibratory motion of the proof masses. The detection ofin-plane deflection is susceptible, however, to errors from drivefeedthrough.

[0038] First and second sensing electrodes 24, 26 are disposed on thesubstrate 32 for detecting the anti-parallel, out-of-plane Coriolisdeflections of the proof masses 20 and 22. The amplitudes of theout-of-plane deflections are proportional to the input rotational rate,according to Eq. 1. The sensor output signals therefore provide ameasure of the rotational rate {right arrow over (Ω)}.

[0039] In one embodiment, capacitive sensing is used. In thisembodiment, each out-of-plane sensing electrode is fixedly positionedwith respect to the substrate 32, and is disposed below a conductiveregion (21 a or 21 b) of a respective one of the first 20 and second 22proof masses. The capacitances between the sensing electrodes 24, 26 andthe proof masses 20, 22 thus oscillate in accordance with the amplitudesof the out-of-plane Coriolis deflections. The sensing electrodesgenerate output signals that are proportional to the separation betweenthe conductive regions 21 a, 21 b, and the associated sensing electrodes24, 26, and hence are proportional to the amplitudes of the Coriolisdeflections of the proof masses. The sensor output signals thus reflectthe changes in the capacitances between the sensing electrodes and theirassociated proof masses, and vary according to the frequency of theout-of-plane oscillations.

[0040] A DC bias voltage V_(b) is applied to the sensing electrodes 24,26 to establish a potential difference. Because of the capacitancesbetween the conductive regions 21 a, 21 b and the associated sensingelectrodes, the sensing electrodes 24, 26 induce on each proof mass acharge that is proportional to the separation between the proof mass andits associated sense electrode. The changes in capacitance between theproof masses 20, 22 and their associated sensing electrodes 24, 26 thusresult in changes in the charge on the proof masses 20, and 22, whichare reflected in the sensor output signals.

[0041] The detection of the out-of-plane deflections is susceptible,however, to errors resulting from drive feedthrough into the sensoroutput signal. In particular, the sensor output signal is contaminatedby capacitive coupling from the drive electrodes. Such capacitivecoupling is caused by parasitic capacitances related to the fabricationand packaging of the sensor system. Drive feedthrough includessynchronous and asynchronous components. Synchronous drive feedthroughincludes signals at the fundamental frequency and its harmonics.Asynchronous drive feedthrough includes all other signals originating atthe drive electrodes. Synchronous feedthrough causes a direct instrumentbias. Asynchronous feedthrough imposes gain limitations and limitsdesensitization of the sensor to DC offsets.

[0042] An off-frequency drive scheme for eliminating synchronousfeedthrough is disclosed in prior art U.S. Pat. Nos. 5,481,914 and5,703,292, both of which are incorporated herein by reference. In thisscheme, the sensor 10 is connected in a feedback relationship with afrequency translation circuit. The input drive signal is converted intoa feedback signal which is further processed to control the drive signalin a closed loop. The frequency translation circuit suppressescomponents of the feedback signal at the resonant frequency of thesensor, by effectively multiplying the feedback signal by a commutationsignal. Any coupling of the drive signal into the sensor output signalis then readily removed by using conventional filtering techniques,since the drive signal now has a frequency different from the frequencyof the sensor output signal. The frequency translation circuit thussubstantially reduces synchronous feedthrough, i.e. in-band coupling ofthe drive signal into the feedback signal and into the sensor outputsignal. The off-frequency drive scheme summarized above still does notremove, however, asynchronous feedthrough.

[0043] The present invention provides a system for substantiallyreducing both synchronous and asynchronous feedthrough. It has beenfound that the dominant cause of drive feedthrough is a mismatch in thecapacitances C₁ and C₂ between the drive electrodes 14, 16 and theirassociated proof masses 20, 22. The difference between C₁ and C₂, whichshould ideally be zero, is the main cause of drive feedthrough. Thepresent invention compensates for variations in C₁ and C₂ by varying thedrive voltages V₁ and V₂ so as to equalize the magnitudes of the chargesQ₁ and Q₂ induced on the first and second proof masses by way of thedrive voltages. The charges are related to the drive voltages by therelation Q=CV, where C is the associated capacitance, C₁ or C₂. Bybalancing out the charges induced on the proof masses, i.e. by renderingthe charges equal and opposite, feedthrough of the drive signals intothe sensor output signals is nulled. In the present invention,compensation for capacitance mismatch is accomplished by measuring oneor more of the drive feedthrough components, and then nulling themeasured components by adjusting the relative amplitudes of the drivesignals V₁, V₂, as explained further below.

[0044] FIGS. 2(a) and 2(b) provides a circuit diagram of a drivecoupling model for the sensor discussed above. In FIG. 2(a), a sensepreamplifier 31 is shown connected to the proof masses 20 and 22. Theproof masses are placed at a virtual ground of the sense preamplifier31. A first C₁ and a second C₂ capacitance is defined between each driveelectrode and the summing node of the sense preamplifier 31.

[0045] Referring to FIG. 2(b), the preamplifier output V₀ is given by:$\begin{matrix}{V_{o} = {{- {C_{f}^{- 1}\lbrack {{V_{1}C_{1}} + {V_{2}C_{2}}} \rbrack}} + {V_{e}\lbrack {1 + ( \frac{C_{1} + C_{2} + C_{N}}{C_{f}} )} \rbrack}}} & {{Eq}.\quad 2}\end{matrix}$

[0046] where V_(e) is the preamplifier input error voltage, which isgenerally small unless the input changes very rapidly, and the voltagesand capacitances are as shown in FIG. 2(b). If the preamplifierbandwidth is made arbitrarily large, the error term becomes arbitrarilysmall, and the preamplifier output is simplified, becoming:

V ₀ =−C _(f) ⁻¹ [V ₁ C ₁ +V ₂ C ₂ ]=−C _(f) ⁻¹ [Q ₁ +Q ₂]  Eq. 3

[0047] where Q₁ and Q₂ represent the charge transferred to the summingnode by C₁ and C₂, respectively. Drive feedthrough in the preamplifieroutput can thus be nulled by effecting a charge balance condition:

Q ₁ =−Q ₂  Eq. 4

[0048] The charge balance condition can be alternatively expressed as:

V ₁ /V ₂ =−C ₂ /C ₁  Eq. 5

[0049] Therefore, if V₁ and V₂ have opposite polarities and a magnituderatio equal to the reciprocal of the ratio of the correspondingcapacitors, drive feedthrough from static capacitance mismatch isnulled.

[0050] In the present invention, drive feedthrough can be measured andnulled in one of several embodiments. In order to measure drivefeedthrough, a signal that is proportional to the drive capacitancemismatch must first be obtained. In one embodiment, a separate tracesignal having a characteristic such as frequency different from thedrive signals, can be obtained from a trace source and added to thedrive signals. The trace signal is separately detected, and used tomeasure drive capacitance mismatch. In another embodiment in which thedrive signal inherently contains components at off-frequencies, as inthe off-frequency drive scheme discussed above, one or more of theinherent off-frequency components of the drive signal can be detectedthat are proportional to the capacitance mismatch. The detectedoff-frequency components are then demodulated in order to measure thecapacitance mismatch. The measured capacitance mismatch is nulled bymaking a fixed adjustment to the differential drive voltages, or with anautomatic feedback servo loop.

[0051]FIG. 3 illustrates one embodiment of the present invention inwhich an off-frequency artifact of the drive signal, i.e. an inherentoff-frequency component of the drive signal, is used to measure thecapacitance mismatch. A nulling compensator 36 is used in conjunctionwith a feedback servo loop 38, to compensate for the measuredcapacitance mismatch. The nulling compensator 36 demodulates theoff-frequency artifact to provide a measure of capacitance mismatch.Based on the measured capacitance mismatch, the differential amplitudeof the drive signals V₁, V₂ is modified so as to effect the chargebalance condition of Eq. 5, thereby substantially reducing drivefeedthrough into the sensor output signal.

[0052] The capacitance mismatch between the drive electrodes 14, 16 andtheir associated proof masses 20, 22 is measured by detecting anoff-frequency artifact of the drive signals V₁, V₂ at the output of thesense preamplifier 31, and demodulating the detected artifact. In oneembodiment of the present invention, the form of the drive signals isdescribed by the following equation: $\begin{matrix}{{{V_{D}(t)} = {( {B + {A\quad s\quad {q( {\omega \quad t} )}}} )s\quad {q( \frac{\omega \quad t}{n} )}}},{n\quad e\quad v\quad e\quad n}} & {{Eq}.\quad 6}\end{matrix}$

[0053] where ω is the fundamental frequency, and sq(ωt) is a zero-meansquare-wave with amplitude=1 volt and period 2π/ω.

[0054] Because of mismatch in the time-average drive capacitance, asmaller version of the signal of Eq. 5 exists, along with other signals,at the preamplifier output. That is, the amplified preamplifier outputis: $\begin{matrix}{{{V_{o}(t)} \approx {{{K( {B + {A\quad s\quad {q( {\omega \quad t} )}}} )}s\quad {q( \frac{\omega \quad t}{n} )}} + {o\quad t\quad h\quad e\quad r\quad s\quad i\quad g\quad n\quad a\quad l\quad s}}},} & {{Eq}.\quad 7}\end{matrix}$

[0055] where the value of K is given by: $\begin{matrix}{K = {G_{A\quad C}( \frac{\Delta \quad C_{D}}{C_{f}} )}} & {{Eq}.\quad 8}\end{matrix}$

[0056] in which G_(AC) is the gain following the preamplification, andΔC_(D) is the mismatch in the time-average drive capacitors.

[0057] The signal of Eq. 6 includes a significant term at frequency ω/n.This term can be synchronously demodulated to yield a DC signal which isproportional to K, and thus proportional to the capacitance mismatch.The sense preamplifier output is multiplied by a square wave 93 offrequency ω/n, in order to eliminate even harmonics of the basicsubharmonic frequency ω/n. The multiplied output is given by:$\begin{matrix}{{V_{m}(t)} = {{{K( {B + {A\quad s\quad {q( {\omega \quad t} )}}} )}s\quad {q^{2}( \frac{\omega \quad t}{n} )}} = {K( {B + {A\quad s\quad {q( {\omega \quad t} )}}} )}}} & {{Eq}.\quad 9}\end{matrix}$

[0058] The modulation components can be filtered out by passing thesignal of Eq. 9 through the low pass filter 52. The result is:

V _(LPF)(t)=KB=G _(AC)(ΔC _(D) /C _(f)) B  Eq. 10

[0059] which is the desired DC signal that provides a measure of thecapacitance mismatch. The capacitance mismatch is thus given by:

ΔC _(D)=(C _(f) V _(LP)(t) /B G _(AC))  Eq. 11

[0060] In the illustrated embodiment, the feedthrough nullingcompensator 36 is used in conjunction with a feedback gain control loop38. The feedback gain control loop is operative to receive a signal 90from the position sensitive pick off 28. The signal 90 is indicative ofthe amplitude of the in-plane displacement of the first 20 and thesecond 22 proof masses. The signal 90 is fed into a frequencytranslation circuit 48, which suppresses components at the fundamentalfrequency of the sensor 10. The frequency translation circuit outputsdrive signals 92 a and 92 b for driving the proof masses of the sensor10.

[0061] In one embodiment, the feedback control loop 38 includes a motorpreamplifier 42, a shifter 44, a summer 46, and the frequencytranslation circuit 48. In one embodiment, the signal 90 is fed to themotor preamplifier 42, the output of which is shifted by ninety degreesin the shifter 44. The output signal from the shifter 44 is summed inthe summer 46 with an amplitude control voltage 91. The output signal 77from the summer 46 is fed to the frequency translation circuit, andmultiplied by a commutation clock signal 79 in order to suppresscomponents in the signal 77 at the resonant frequency of the sensor 10.The output 99 from the frequency translation circuit 48 is then splitinto first and second opposite phase drive signals 92 a and 92 b fordriving the proof masses 20 and 22.

[0062] The output from the LPF 52 (Eq. 10), which is proportional to thecapacitance mismatch, is integrated in the integral controller 54. Theoutput signal from the integrated controller 54 is split into twosignals, one of which is inverted in the amplifier 56. The split signalsprovide opposite-phase control signals 94 a and 94 b, which are used tocontrol the VGAs 58 a and 58 b respectively, thus closing the automaticfeedback servo loop. The common-mode gain of the VGAs, controlled by thedrive signals 92 a and 92 b from the frequency translation circuit 48,remains constant.

[0063] The differential gain of the VGAs 58 a and 58 b is adjusted bythe control signals 94 a and 94 b according to the measured capacitancemismatch. In response to the control signals 94 a and 94 b, the VGAs 58a and 58 b adjust the ratio of the amplitudes of the first and seconddrive signals to be equal to the reciprocal of the ratio of the first C₁and second C₂ capacitances. The charge balance condition of Eq. 4 andEq. 5 is thus achieved, so that drive feedthrough in the sensepreamplifier output is automatically and continuously nulled. Themagnitude adjusted drive signals V₁ and V₂, shown in FIG. 3, aredelivered to the drive electrodes 14 and 16 through the VGAs 58 a and 58b.

[0064] It will be noted that the techniques described above have generalapplicability. Many forms of drive feedthrough can be nulled using thetechniques described above. It should therefore be understood that theinvention is not limited to the particular embodiment shown anddescribed herein, and that various changes and modifications may be madewithout departing from the spirit and scope of this concept as definedby the following claims.

What is claimed is:
 1. A sensor for detecting a rotational rate about aninput axis of said sensor, comprising: A. a substrate; B. a first proofmass and a second proof mass positioned on opposite sides of an inputaxis, each of said first and second proof masses being flexurallycoupled to said substrate so as to permit an in-plane vibratory motionin a nominal plane including said input axis and an out-of-planevibratory motion in a direction perpendicular to said nominal plane,each of said proof masses including an electrically conductive region;C. a driver including (i) a first drive electrode opposite saidelectrically conductive region of said first proof mass, (ii) a seconddrive electrode opposite said electrically conductive region of saidsecond proof mass, said first and second drive electrodes being adaptedto receive an associated one of first and second a.c. opposite phaseelectrical drive signals for electrostatically driving said first andsecond proof masses to effect anti-parallel vibration of said proofmasses in said nominal plane, a first capacitance being defined betweenthe first drive electrode and the first proof mass, and a secondcapacitance being defined between the second drive electrode and thesecond proof mass; D. a first sensing electrode and a second sensingelectrode for detecting said vibratory motion perpendicular to saidnominal plane, each sensing electrode being fixedly positioned withrespect to said substrate and disposed opposite to said electricallyconductive region on a respective one of said first and second proofmasses; E. means for adjusting the relative amplitudes of said first andsecond a.c. drive signals whereby the ratio of said amplitudes isproportional to the ratio of said first and second capacitances; and F.a circuit for generating an output signal representative of theseparation between said sensing electrodes and said conductive regionsof said proof masses opposite thereto, said signal being representativeof said rotational rate about said input axis; wherein said adjustmentof relative amplitudes of said first and second a.c. drive signalssubstantially nulls drive feedthrough in said output signal caused by amismatch in said first and second capacitances.
 2. A sensor according toclaim 1 further including a position sensitive pick-off electrode fordetecting said in-plane vibratory motion, said in-plane sensingelectrode being disposed between said first proof mass and said secondproof mass.
 3. A sensor according to claim 1 wherein the frequency ofsaid drive signals is substantially equal to a fundamental frequencycorresponding to a mechanical resonant frequency of the sensor.
 4. Asensor according to claim 1 wherein said drive electrodes, said sensingelectrodes, and said proof masses are made from an etched siliconstructure.
 5. A sensor according to claim 1 wherein said circuitincludes an adjustment device responsive to a controller for effectingsaid ratio of amplitudes.
 6. A sensor according to claim 1 wherein saidcircuit includes a servo loop for adaptively effecting said ratio ofamplitudes.
 7. A sensor according to claim 1 wherein said circuitcomprises first and second circuits, and wherein: (a) said first circuitis operative to provide a signal indicative of a capacitance mismatchbetween said first and second capacitances; and (b) said second circuitis operative to measure said capacitance mismatch and to compensate forsaid measured capacitance mismatch by adjusting said first and secondopposite phase drive signals, and to thereby substantially null drivefeedthrough based on said measured capacitance mismatch.
 8. A sensoraccording to claim 7 wherein said first circuit includes a sensepreamplifier connected to the proof masses, said sense preamplifierhaving an output.
 9. A sensor according to claim 7 wherein saidindicative signal comprises a separate tracer signal added to said drivesignals.
 10. A sensor according to claim 7 wherein said second circuitcomprises: (a) an adjustment device responsive to a controller foreffecting said ratio of amplitudes; and (b) a servo loop for adaptivelyeffecting said ratio of amplitudes
 11. A sensor according to claim 7wherein the frequency of said drive signals is substantially equal to afundamental frequency corresponding to a mechanical resonant frequencyof the sensor, and wherein said indicative signal comprises aoff-frequency artifact in which components of said drive signals at saidfundamental frequency have been suppressed.
 12. A sensor according toclaim 11 wherein said first circuit includes a sense preamplifierconnected to the proof masses, said sense preamplifier having an output,and wherein said second circuit includes means for demodulating saidoff-frequency artifact.
 13. A sensor according to claim 12 wherein saidmeans for demodulating said off-frequency artifact comprises amultiplier connected to said output of said preamplifier, and a low passfilter for removing modulation components in said off-frequencyartifact.
 14. A sensor according to claim 10 wherein a control signalfrom the controller is operable to be split into first and secondcontrol signals of opposite phase.
 15. A sensor according to claim 14wherein said adjustment device includes first and second variable gainamplifiers interposed between said servo loop and said first and seconddrive electrodes, said variable gain amplifiers being operative toadjust the differential amplitude of the drive signals in response tosaid first and second control signals.
 16. A sensor according to claim 1wherein the first and second drive electrodes and the pick-off electrodeinclude comb electrodes, further wherein the first proof mass has combelectrodes interleaved with the first drive electrode comb electrodes ona first side and comb electrodes interleaved with the pick-off combelectrodes on a second side, and wherein the second proof mass has combelectrodes interleaved with the second drive electrode comb electrodeson a first side and comb electrodes interleaved with the pick-off combelectrodes on a second side.
 17. A system for nulling feedthrough errorin a sensor, the system comprising: (a) a source of a drive signal, anda further signal having characteristics different from the drive signal,the drive signal and the further signal being applied to drive thesensor, wherein the further signal can be detected separately from thedrive signal; (b) means for detecting a response of the sensor to thedrive applied thereto; and (c) means, responsive to components of thefurther signal in the detected response, for adjusting the drive signalso as to diminish the feedthrough error.
 18. A system according to claim17, wherein said means for adjusting the drive signal is responsive to acontroller.
 19. A system according to claim 18, wherein said means foradjusting the drive signal includes a feedback servo loop.
 20. A systemaccording to claim 17, wherein said sensor includes at least two driveelectrodes having associated drive capacitances and being adapted toreceive equal and opposite-phase drive signals.
 21. A system accordingto claim 20, wherein said feedthrough error is caused at least in partby a mismatch between said at least two drive capacitances.
 22. A systemaccording to claim 21, wherein said further signal provides a measure ofsaid capacitance mismatch
 23. A method for nulling drive feedthrough ina sensor having first and second drive electrodes which impart vibratorymotion to first and second members in response to drive signals, a firstcapacitance being defined between the first drive electrode and thefirst member, and a second capacitance being defined between the seconddrive electrode and the second member, the method comprising the stepsof: (a) measuring a mismatch between said first capacitance and saidsecond capacitance; and (b) compensating for said capacitance mismatch,thereby nulling drive feedthrough caused by said mismatch.
 24. A methodaccording to claim 23 wherein said measuring step includes adding aseparate trace signal to the drive signals.
 25. A method according toclaim 23 wherein said measuring step includes demodulating an inherentoff-frequency artifact of the drive signals.
 26. A method according toclaim 25 wherein the demodulating step includes multiplying an amplifiedpreamplifier output by a square wave of frequency ω/n to provide a firstintermediate output, said amplified preamplifier output having the form:${{V_{o}(t)} \approx {{K( {B + {A\quad s\quad {q( {\omega \quad t} )}}} )}s\quad {q( \frac{\omega \quad t}{n} )}}},$

whereby K is proportional to said capacitance mismatch, and furtherwherein the demodulating step further includes passing the firstintermediate output through a low pass filter to remove modulationcomponents and provide a signal that is proportional to the capacitancemismatch and that has the form: V _(LPF)(t)=KB.
 27. A method accordingto claim 23 wherein said step of compensating for said capacitancemismatch includes adjusting a drive signal amplitude.
 28. A methodaccording to claim 27 wherein said adjusting step includes adjusting adifferential drive signal amplitude in a system having first and seconddrive signals associated with the first and second drive electrodes,respectively.
 29. A method according to claim 28 wherein said first andsecond drive signals are a.c. opposite phase signals.
 30. A methodaccording to claim 28 wherein the adjusting step includes fixing thefirst and second drive signals at respective predetermined levels.
 31. Amethod according to claim 28 wherein the adjusting step includesservoing the first and second drive signals so as to adaptively effectan adjustment of respective drive signal amplitudes.